% Source = http://acm.math.spbu.ru/cgi-bin/monitor.pl/m051006.dat, problem E

\begin{problem}{Discrete Logging}{logging.in}{logging.out}{3 seconds}{256 mb}

\begin{center}
\includegraphics[width=6.5cm]{pics/logging.jpg}
\end{center}

Given a prime $P$, $2 \le P < 2^{31}$, an integer 
$B$, $2 \le B < P$, and an integer $N$, $2 \le N < P$, compute the 
discrete logarithm of $N$, base $B$, modulo $P$. That is, find an integer 
$L$ such that $B^L \equiv N (\mod P)$.

\InputFile

Read several lines of input, each containing $P$,$B$,$N$ 
separated by a space.

\OutputFile

For each line print the logarithm on a separate 
line. If there are several, print the smallest; if 
there is none, print ``\texttt{no solution}''. 

\Example

\begin{example}
\exmp{
5 2 1
5 2 2
5 2 3
5 2 4
5 3 1
5 3 2
5 3 3
5 3 4
5 4 1
5 4 2
5 4 3
5 4 4
12345701 2 1111111
1111111121 65537 1111111111
}{
0
1
3
2
0
3
1
2
0
no solution
no solution
1
9584351
462803587
}%
\end{example}

\end{problem}

